Translation Math


Translation math, is kind of transformation math. In translation, object’s shape is not supposed to change but location of quadrants can change according to translation factor. New coordinates may lie in any of four quadrants and so resultant figure can be positioned in any of the four quadrants. Shape would not change means dimensions of object to be translated will not be affected. The translated geometry of any figure will give an identical geometrical shape.
Let us consider some examples to understand the meaning of translation in math.

Example: Suppose we have a square whose coordinates are given as follows:
A (2, 4), B (6, 4), C (2, 8) and D (6, 8)
If x - coordinates are translated by 4 units and y – coordinate by -4 units, what will be new location of square?

Solution: To solve this problem of translations math we would add or subtract translation factor for ‘x’ and ‘y’ coordinates respectively to each of ‘x’ and ‘y’ values of given coordinates. So, new coordinates of square are:
A’ (2 + 4, 4 - 4), B’ (6 + 4, 4 - 4), C’ (2 + 4, 8 - 4) and D’ (6 + 4, 8 - 4)
A’ (6, 0), B’ (10, 0), C’ (6, 4) and D’ (10, 4)

Thus, new square is located in first quadrant only with one side coinciding with y – axis. If we check area of square formed after translation, we would see that, it is equal to that of original square. Initial side of square was 4 units and after translation it is same. Thus, area is 16 square units for both squares.

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